A conventional mop assembly includes a mop handle attached to a mop head. In most cases a separate cleaning pad is removably attached to the mop head, enabling it to be removed for periodic cleaning or replacement. Various removable attachment assemblies are known, for example, hook and loop type fastener strips that have oppositely positioned cooperating portions mounted on the mop head and on the mop pad, respectively. One prior art mop head has a bottom face plane formed by a web structure. Hook and loop type fastener strips are mounted in recessed corner regions of the bottom face of the mop head. The bottom faces of the fastener strips protrude outwardly beyond the bottom face plane of the mop head.